Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Answer 1

We want $p-1$ to divide $p+p+p-k$, i.e. $3p-k$.

So, assume that we have a number $\alpha$ such that

$\dfrac{3p-k}{p-1}=\alpha$

This implies that

$3p-k=\alpha(p-1)=\alpha p-\alpha$

Those two expression are equal if the correspondent coefficients are equal:

$3p-k=\alpha p-\alpha \iff \begin{cases}3=\alpha\\-k=-\alpha\end{cases}\iff \begin{cases}3=\alpha\\k=\alpha\end{cases}$

And it should be immediate to conclude the value for k from here.

Answer 2

Answer: none because i wont give it sped

r